By mid-day on a Tuesday, Goose Island will more than likely be full, as it is often full by 8 or 9 in the morning. Up river on UT 128, Big Bend had some larger sites that might be available.
South of Moab, Kens Lake has a number of spots for larger rigs. Not much shade and many are very exposed when windy. Don't get your hopes up by the word "lake" as it can be pretty low in the fall. Advantage is proximity to town.
Sand Flats east above Moab is run by the county and has 30 sites for larger rigs. Popular with the mountain biking crowd.
A bit further afield is Horsethief CG on UT 313 on the road up to Dead Horse Point SP. Generally better spacing and privacy up there, plus a little cooler. More of the sites are capable of handling your size rig. Has been "discovered" so also gets full nowadays. Closer to Canyonlands than the others but further from Arches and Moab.
If all of the above are filled, try Ledges CG up Kane Creek Road past McDonalds. Last five miles of the road are graded gravel and can be quite washboard-y. But except on busy weekends, there are usually spots there.